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One of the most complex tasks of decision making and planning is to gatherinformation. This task becomes even more complex when the state ishigh-dimensional and its belief cannot be expressed with a parametricdistribution. Although the state is high-dimensional, in many problems only asmall fraction of it might be involved in transitioning the state andgenerating observations. We exploit this fact to calculate aninformation-theoretic expected reward, mutual information (MI), over a muchlower-dimensional subset of the state, to improve efficiency and withoutsacrificing accuracy. A similar approach was used in previous works, yetspecifically for Gaussian distributions, and we here extend it for generaldistributions. Moreover, we apply the dimensionality reduction for cases inwhich the new states are augmented to the previous, yet again withoutsacrificing accuracy. We then continue by developing an estimator for the MIwhich works in a Sequential Monte Carlo (SMC) manner, and avoids thereconstruction of future belief's surfaces. Finally, we show how this work isapplied to the informative planning optimization problem. This work is thenevaluated in a simulation of an active SLAM problem, where the improvement inboth accuracy and timing is demonstrated.

involve-MI: Informative Planning with High-Dimensional Non-Parametric Beliefs